Physical Sciences and Mathematics Commons^™

Portfolio Optimization Analysis In The Family Of 4/2 Stochastic Volatility Models, Yuyang Cheng

Electronic Thesis and Dissertation Repository

Over the last two decades, trading of financial derivatives has increased significantly along with richer and more complex behaviour/traits on the underlying assets. The need for more advanced models to capture traits and behaviour of risky assets is crucial. In this spirit, the state-of-the-art 4/2 stochastic volatility model was recently proposed by Grasselli in 2017 and has gained great attention ever since. The 4/2 model is a superposition of a Heston (1/2) component and a 3/2 component, which is shown to be able to eliminate the limitations of these two individual models, bringing the best out of each other. Based …

Statistical Roles Of The G-Expectation Framework In Model Uncertainty: The Semi-G-Structure As A Stepping Stone, Yifan Li

Electronic Thesis and Dissertation Repository

The G-expectation framework is a generalization of the classical probability system based on the sublinear expectation to deal with phenomena that cannot be described by a single probabilistic model. These phenomena are closely related to the long-existing concern about model uncertainty in statistics. However, the distributions and independence in the G-framework are quite different from the classical setup. These distinctions bring difficulty when applying the idea of this framework to general statistical practice. Therefore, a fundamental and unavoidable problem is how to better understand G-version concepts from a statistical perspective.

To explore this problem, this thesis establishes a new substructure …

Regression-Based Methods For Dynamic Treatment Regimes With Mismeasured Covariates Or Misclassified Response, Dan Liu

Electronic Thesis and Dissertation Repository

The statistical study of dynamic treatment regimes (DTRs) focuses on estimating sequential treatment decision rules tailored to patient-level information across multiple stages of intervention. Regression-based methods in DTR have been studied in the literature with a critical assumption that all the observed variables are precisely measured. However, this assumption is often violated in many applications. One example is the STAR*D study, in which the patient's depressive score is subject to measurement error. In this thesis, we explore problems in the context of DTR with measurement error or misclassification considered in the observed data.

The first project deals with covariate measurement …

Copulas, Maximal Dependence, And Anomaly Detection In Bi-Variate Time Series, Ning Sun

Electronic Thesis and Dissertation Repository

This thesis focuses on discussing non-parametric estimators and their asymptotic behaviors for indices developed to characterize bi-variate time series. There are typically two types of indices depending on whether the distributional information is involved. For the indices containing the distributional information of the bivariate stationary time series, we particularly focus on the index called the tail order of maximal dependence (TOMD), which is an improvement of the tail order. For the indices without distributional information of the bivariate time series, we focus on an anomaly detection index for univariate input-output systems.

This thesis integrates three articles. The first article (Chapter …

An Analysis Of Weighted Least Squares Monte Carlo, Xiaotian Zhu

Electronic Thesis and Dissertation Repository

Since Longstaff and Schwartz [2001] brought the amazing Regression-based Monte Carlo (LSMC) method in pricing American options, it has received heated discussion. Based on the research done by Fabozzi et al. [2017] that applies the heteroscedasticity correction method to LSMC, we further extend the study by introducing the methods from Park [1966] and Harvey [1976]. Our work shows that for a single stock American Call option modelled by GBM with two exercise opportunities, WLSMC or IRLSMC provides better estimates in continuation value than LSMC. However, they do not lead to better exercise decisions and hence have little to no effect …

New Developments On The Estimability And The Estimation Of Phase-Type Actuarial Models, Cong Nie

Electronic Thesis and Dissertation Repository

This thesis studies the estimability and the estimation methods for two models based on Markov processes: the phase-type aging model (PTAM), which models the human aging process, and the discrete multivariate phase-type model (DMPTM), which can be used to model multivariate insurance claim processes.

The principal contributions of this thesis can be categorized into two areas. First, an objective measure of estimability is proposed to quantify estimability in the context of statistical models. Existing methods for assessing estimability require the subjective specification of thresholds, which potentially limits their usefulness. Unlike these methods, the proposed measure of estimability is objective. In …

Early-Warning Alert Systems For Financial-Instability Detection: An Hmm-Driven Approach, Xing Gu

Electronic Thesis and Dissertation Repository

Regulators’ early intervention is crucial when the financial system is experiencing difficulties. Financial stability must be preserved to avert banks’ bailouts, which hugely drain government's financial resources. Detecting in advance periods of financial crisis entails the development and customisation of accurate and robust quantitative techniques. The goal of this thesis is to construct automated systems via the interplay of various mathematical and statistical methodologies to signal financial instability episodes in the near-term horizon. These signal alerts could provide regulatory bodies with the capacity to initiate appropriate response that will thwart or at least minimise the occurrence of a financial crisis. …

Flexible Modelling Of Time-Dependent Covariate Effects With Correlated Competing Risks: Application To Hereditary Breast And Ovarian Cancer Families, Seungwoo Lee

Electronic Thesis and Dissertation Repository

This thesis aims to develop a flexible approach for modelling time-dependent covariate effects on event risk using B-splines in the presence of correlated competing risks. The performance of the proposed model was evaluated via simulation in terms of the bias and precision of the estimation of the parameters and penetrance functions. In addition, we extended the concordance index to account for time-dependent effects and competing events simultaneously and demonstrated its inference procedures. We applied our proposed methods to data rising from the BRCA1 mutation families from the breast cancer family registry to evaluate the time-dependent effects of mammographic screening and …

Statistical Applications To The Management Of Intensive Care And Step-Down Units, Yawo Mamoua Kobara

Electronic Thesis and Dissertation Repository

This thesis proposes three contributing manuscripts related to patient flow management, server decision-making, and ventilation time in the intensive care and step-down units system.

First, a Markov decision process (MDP) model with a Monte Carlo simulation was performed to compare two patient flow policies: prioritizing premature step-down and prioritizing rejection of patients when the intensive care unit is congested. The optimal decisions were obtained under the two strategies. The simulation results based on these optimal decisions show that a premature step-down strategy contributes to higher congestion downstream. Counter-intuitively, premature step-down should be discouraged, and patient rejection or divergence actions should …

Testing Aftershock Forecasts Using Bayesian Methods, Elisa Dong

Electronic Thesis and Dissertation Repository

The presence of strong aftershocks can increase the seismic hazard following a large earthquake and should be considered for operational earthquake forecasting and risk management. Aftershock forecasts are generated from seismicity models during the evolution of the aftershock sequence. This work compares quantitative test results of the forecasting abilities for three competing aftershock rate models - the modified Omori law, the Epidemic Type Aftershock Sequence model, and the compound Omori law - to identify the best performing model for forecasting the largest aftershock during the early aftershock sequence. Forecasts of large aftershock probabilities are generated by either the Extreme Value …

Physical Investigation Of Downburst Winds And Applicability To Full Scale Events, Federico Canepa

Electronic Thesis and Dissertation Repository

Thunderstorm winds, i.e. downbursts, are cold descending currents originating from cumulonimbus clouds which, upon the impingement on the ground, spread radially with high intensities. The downdraft phase of the storm and the subsequent radial outflow that is formed can cause major issues for aviation and immense damages to ground-mounted structures. Thunderstorm winds present characteristics completely different from the stationary Gaussian synoptic winds, which largely affect the mid-latitude areas of the globe in the form of extra-tropical cyclones. Downbursts are very localized winds in both space and time. It follows that their statistical investigation, by means of classical full scale anemometric …